{{In 1927 David Hilbert gave a talk at Hamburg university, where heexplained his opinions about the foundations of mathematics.}} It is agreat honour and at the same time a necessity for me to round out anddevelop my thoughts on the foundations of mathematics, which wasexpounded here one day five years ago {{compare Kalenderblatt 101212to 101214http://www.hs-augsburg.de/~mueckenh/KB/}} and which since then have constantly kept me most activelyoccupied. With this new way of providing a foundation for mathematics,which we may appropriately call a proof theory, I pursue a significantgoal, for I should like to eliminate once and for all the questionsregarding the foundations of mathematics [...] I have already set forth the basic features of this proof theory ofmine on different occasions, in Copenhagen [1922], here in Hamburg[1922], in Leipzig [1922], and in Münster [1925]; in the meantime muchfault has been found with it, and objections of all kinds have beenraised against it, all of which I consider just as unfair as it canbe. [...] Poincaré already made various statements that conflict with myviews; above all, he denied from the outset the possibility of aconsistency proof for the arithmetic axioms, maintaining that theconsistency of the method of mathematical induction could never beproved except through the inductive method itself. [...] RegrettablyPoincaré, the mathematician who in his generation was the richest inideas and the most fertile, had a decided prejudice against Cantor'stheory, which prevented him from forming a just opinion of Cantor'smagnificent conceptions. Under these circumstances Poincaré had toreject my theory, which, incidentally, existed at that time only inits completely inadequate early stages. Because of his authority,Poincaré often exerted a one-sided influence on the youngergeneration. {{Not to a sufficient degree, unfortunately. --- ThenHilbert discusses the objections by Russell and Whitehead and finallyBrouwer. Hilbert concludes:}} I cannot for the most part agree withtheir tendency; I feel, rather, that they are to a large extent behindthe times, as if they came from a period when Cantor's majestic worldof ideas had not yet been discovered. {{A world discovered by a manwho was behind his times, who did not recognize atoms in the late 19thcentury, but rejected evolution, who believed in an infinite set ofangels and took the basis of his mathematics from the holy bible: "ininfinity and beyond".}}[E. Artin et al. (eds.): "D. Hilbert: Die Grundlagen derMathematik" (1927). Abh. Math. Seminar Univ. Hamburg, vol. 6, Teubner,Leipzig (1928) 65-85. English translation: J. van Heijenoort: "FromFrege to Gödel", Harvard Univ. Press, Cambridge, Mass. (1967) 464-479]